Mathlib Map

Theorems · Definition · category theory

TopPair.Hom.fst

{X Y : TopPair} → (X ⟶ Y) → (TopPair.fst ⟶ TopPair.fst)

The map between the first spaces

Defined in
Mathlib.Topology.Category.TopPair
Cited by
16 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopPair.Homotopy.fst · cited by 12Homotopy.fstTopPair.Homotopy.ext · cited by 3Homotopy.extTopPair.Homotopy.refl · cited by 3Homotopy.reflTopPair.Hom.w · cited by 2Hom.wTopPair.Homotopy.w · cited by 2Homotopy.wTopPair.Homotopy.symm_fst · cited by 1Homotopy.symm_fstTopPair.Homotopy.w_apply · cited by 1Homotopy.w_applyTopPair.Homotopy.mk.inj · cited by 1mk.injTopPair.Homotopy.mk.noConfusion · cited by 1mk.noConfusionTopPair.Homotopy.mk.sizeOf_spec · cited by 0mk.sizeOf_specTopPair.Homotopy.casesOn · cited by 0Homotopy.casesOnTopPair.Homotopy.comp_fst · cited by 0Homotopy.comp_fstTopPair.Homotopy.ext_iff · cited by 0Homotopy.ext_iffTopPair.Homotopy.noConfusion · cited by 0Homotopy.noConfusionTopPair.Homotopy.noConfusionType · cited by 0Homotopy.noConfusionTypeQuiver.Hom · cited by 32603Quiver.HomTop.top · cited by 9680Top.topCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…TopCat · cited by 1889TopCatCategoryTheory.CommaMorphism.right · cited by 391CommaMorphism.rightTopCat.isEmbedding · cited by 67TopCat.isEmbeddingTopPair · cited by 67TopPairCategoryTheory.MorphismProperty.Comma.Hom.hom · cited by 45Hom.homTopPair.fst · cited by 21TopPair.fstHom.fstCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.